I see this more often:
I get a black screen most of the time, with a "pretty background" about 1 in 10
or so.
In addition, the size of the window listing login names (and the one with the
password prompt) varies in width: sometimes it is "comfortably wide" allowing
for the circles as I enter my 28 character pass phrase, and sometimes it is
"skinny", allowing for only about 15 or so such circles.

The 'wide' gdm login screens show a 'suspend' button, the 'narrow' ones do not.
Not sure why this would change on different logins to the same machine....
I'll attach below 3 photos of login screen for same system:
First: nice background, wide login screen.
Second: no background, wide login screen.
Third: no background, narrow login screen (no suspend button).
In terms of probability of occurrence: the first is about 10%, the second and
third occur about 45% each.

The background problem should be fixed now, as should the width. The suspend button not showing up is a race that I'll fix by twiddling the startup order of the desktop files. This should show up in rawhide soon. Marking fixed.